To solve this question, we need to remark that the total segment is AC = 20, and the sum of the segments AB + BC = AC. Then, we have that:
[tex]AB+BC=AC\Rightarrow(2x+1)+(8x-1)=20[/tex]
Thus, we have to sum the like terms, and simplify the equation:
[tex]2x+8x+1-1=20\Rightarrow10x+0=20\Rightarrow x=\frac{20}{10}\Rightarrow x=2[/tex]
Because x = 2, and BC = 8x - 1, then BC = 8 * (2) - 1 ---> BC = 10 - 1 ---> BC = 9.
Therefore, the length of BC = 9.
